Uncertainty principles for the fractional quaternion fourier transform

The Fractional Quaternion Fourier transform (FrQFT) is a generalization of the usual Quaternion Fourier Transform F-Q. The aim of this paper is to prove some qualitative and quantitative uncertainty principles for FrQFT. The first result consists the Hardy's and an L-p - L-q-version of Miyachi's theorems for the FrQFT, which estimates the decay of two fractional quaternion Fourier transforms F-i,j(alpha)[f] and F-i,j(gamma)[f] with gamma(k)-alpha(k) not equal n pi, for all n is an element of Z with k = 1, 2. The second result consists an extension of Faris' local uncertainty principle for the FrQFT. From our results we deduce the usual uncertainty principles for the FrQFT which states these theorems between a function f and its Fractional Quaternion Fourier Transform F-i,j(gamma)[f].